Can you define "free will"? By "free will" do you mean if he had "free will" we can flap our arms and fly? Or are you referring to free will in terms of Soteriology/Salvation?
Can unregenerate man choose to freely do good? No way, his will is not free. He is in submission to sin.
Here comes a wall of text but by reading only the first 2 paragraphs you should have your answer.
Free will vs. Free Agency
Visitor: What's the difference between freewill and free-agency?
Response: While descriptions may vary, I find the following explanation to be helpful. When it is said that people have no "free will" it does not mean that a person is coerced from the outside and must act against his will. Let that be clear up front. With this in mind, it is important that we learn to distinguish coersion vs. necessity. We are indeed free of external coersion but not free of necessity. Let me explain:
What we mean by denying a (fallen) person has free will is that he/she will act, by necessity, according to the corruption of his/her nature. They are in bondage to sin meaning the love of God and His law are not the unregenerate persons' deepest animating motive and principle (nor is it his motive at all), in anything he does. No one is coercing a sinner to act as they do. Man eagerly volunteers his submission to sin. This means, the unregenerate person will always choose according to who they are by nature, driven by their disposition. In other words, our choices are all voluntary, but we are not free to choose otherwise because we will not understand spiritual things (1 Cor 2:14) and indeed are hostile to them, according to Scripture. Men love darkness and hate the light and will not come into the light (John 3:19, 20) Without the Holy Spirit, man, by nature, is hostile to Christ. In other words, we are in bondage to sin until Christ sets us free. Jesus himself says that a bad tree cannot bear good fruit, that a thornbush cannot bear figs. Jesus is teaching us that the nature of a thing determines BY NECESSITY (not coersion) the direction he/she will take.
Consider the concept of free will by applying it to God Himself. If freedom were defined as the freedom to choose otherwise, let us ask ourselves, does God have such freedom to choose otherwise? In other words, can God freely choose to do good or evil as He pleases? No, of course not. God in his essence is holy and therefore, by definition, cannot sin or be unholy. If he sinned or broke His sure promise He would no longer be God. The same kind of example can be applied to the glorified saints in heaven. God has sealed them in righteousness and they can no longer sin, and more than this, they have no ability to sin or choose otherwise. Yet we consider them the MOST free of all creatures.
Thus the Bible defines freedom, not as the freedom to choose otherwise in any way we please (contrary to our innate disposition), but as holiness, freedom from sin. Read Romans chapter 6. When Jesus says He will set people free, He does not say they are now free to choose good or evil but He will set them free from the bondage of sin. And where there is bondage, by definition there is no freedom. Yes we have free agency, that is, we can voluntarily choose according to our desires, but because our desires are in bondage to corruption of nature this is not freedom in the Biblical sense. Liberation of the will occurs when the Holy Spirit acts to free us.
Consider the opposite theological position which affirms that God elects people based on some kind of forseen faith. If God already knows who will be saved even before He creates them, then such a reality (their salvation) is fixed and cannot be otherwise. Thus God would be wasting His time to try to convert persons whom He knows will never come to faith. Synergists say that God is trying to save every man, yet such a position is untenable if God already knows who is to be saved, that is, unless you are willing to concede that God is not omniscient, but then you would be denying that He is indeed God.
If God knows the end from the beginning exhaustively then He knows who will be saved even prior to creating them. There is certainty here, an unchangable certainty. An additional problem with this is that it means that there is no real free will in this Arminian foreseen faith position because the future is already certain and cannot be otherwise. Yet in this same view God does not determine this future, and thus something else, like Fate perhaps, determines who will believe. The position is so untenable that many traditional Arminians have fled to become open theists who believe God has no exhaustive foreknowledge of the future. But this heretical view will not stand and is sub-Christian.
Hope this helps
jwh
Source
So men can exercise their "free agency" but just not when it comes to salvation? Also, can you explain how God changed man's condition of will before pre-Crucifixion and post? You use the terms will and agency at...your own will...agency, err...Heh. 
Anyway, I'm stepping back before this debate really explodes. Read what William Lane Craig writes, he is a scholar, I am not. I am just your brother (or Sister) in Christ and if you want, I have two mp3 debates between Dr. Michael Brown and Calvinist Dr. James White. I have listened to both debates at least 3 times each. Dr. Brown is not an Arminian or Molinist. Again, if you want them, I'll upload them because they are hard to find.
@ewoksrule: If you want to answer my questions, you can PM me.